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Annales de la Fondation Louis de Broglie, Volume 39, 2014
155
A possible catalytic nuclear fusion
owing to weak interactions
Georges Lochak
Fondation Louis de Broglie 23, rue Marsoulan – 75012 – Paris
email: [email protected]
ABSTRACT. We examine a possible way to avoid the super-high temperatures that are generally introduced in nuclear fusion experiments
in order to overcome the Coulomb barrier between electrically charged
particles of the same sign. We start from the observation that although
temperatures are very high in the hearts of stars, they are lower than
the temperatures used in terrestrial experiments in nuclear fusion. We
suggest the possibility of a catalyst that could be present in stars and
absent from our experiments. It will be shown that neutrinos, in the
stars, could play the role of this catalyst, since they are very abundant and subject to weak interactions, that enables them to play this
role. But they cannot do so in terrestrial experiments, firstly because
there are too few of them, and secondly because since they have no
charge, they are scattered in all directions. Nevertheless, instead of
neutrinos, we have at our disposal leptonic magnetic monopoles which
were at first theoretically discovered and described and have now for
many years been experimentally produced, observed and applied (see
Part III and the references). These leptonic monopoles have the same
weak interactions properties as neutrinos and could accelerate such
phenomena as a proton-proton fusion at temperatures far lower than
the temperatures used in other attempts at nuclear fusion. In addition,
they can easily be focused and accelerated thanks to their magnetic
charge, rather than being scattered in space. Thus they are potentially
able to modify the problem of nuclear fusion.
I. Introduction
One of the most difficult problems in applied physics today is the
industrial development of nuclear fusion energy. As is well known, attempts at present are based on a race to giant temperatures of plasma
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G. Lochak
(sevral hundreds of million degrees) in order to increase the velocity of
nucleons with the same sign of charge, sufficiently to bring them near
enough to each other to overcome the Coulomb repulsion. But there are
two difficulties.
Firstly, there is no material enclosure that can survive such temperatures. The Tokamak of Tamm and Sakharov seemed to provide an
answer : in it, electrically charged particles are obliged to rotate around
a magnetic field to prevent them from approaching the walls. But then a
second difficulty arises, namely that at high temperatures the Tokamak
becomes unstable and works only for brief intervals of time ; thus, the
problem is not solved.
The reason for the present paper is that I think that the high temperatures must be abandoned. But how ? Let us start from a few remarks.
1. Astrophysicists have discovered that although temperatures inside
stars are very high, they are lower than those used in the terrestrial
research installations for nuclear fusion. So I think that it is natural
to ask whether there is not some catalyst in the stars that boosts
fusion, but which would be absent from terrestrial laboratories.
2. What could such a catalyst be ? It is interesting to observe that
weak interactions constitute, in some manner, an obstacle to the
strong interactions that are the sources of the energy of stars. For
instance, they are in a position to slow down the carbon and hydrogen cycles. Thus one can ask if, conversely, they could speed
up the strong interactions, and whether we could make use of this
property.
3. The weak interactions that occur in the known astronomical cycles
leads to the emission of neutrinos. Conversely, in the stars there
are many antineutrinos produced by the β disintegration of free
neutrons :
n → p + e− + ν̃
(1)
Consequently these antineutrinos can be absorbed in inverse β disintegration :
p + ν̃ → n + e+
(2)
In this last reaction, an antineutrino coming from outside gives
rise to the reaction (2) : its absorption is equivalent to the forced
emission of a neutrino. Such a reaction can boost an entire cycle,
the antineutrino playing the role of a quasi-catalyst (only “ quasi ”
because it disappears in the reaction).
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4. Unfortunately, even if this hypothesis is justified, it cannot be applied in laboratories, in which there are not enough neutrinos. Furthermore, since neutrinos are neutral, they are diffused in all directions and cannot be focused. This is one of the reasons for which
the famous experiment of F. Reines & C. Cowan [20], which proved
the existence of the neutrino, was very difficult.
5. Nevertheless, a result due to Ivoilov [21] lends support to this hypothesis ; he showed that when irradiating a β radioactive source with
leptonic magnetic monopoles, the life time of the source decreases,
in other words the β radioactivity is accelerated.
II. A possible catalyst for nuclear fusion
Now, we shall show that a possible catalyst for nuclear fusion may
be the leptonic nuclear monopoles that were theoretically predicted and
then observed in our group [4, 7, 8, 10, 16, 17]. This theory is summarized
in Part III of this paper, and developed – together with descriptions of
experiments – in many other papers [10, 16, 21]. For now let us say
briefly that these monopoles are very light (even massless in the present
theory), contrary to the monopoles described by other authors, which are
supposed to be very heavy. Furthermore, they have two main properties :
a) They have a magnetic charge g equal to 137/2 times the electron
charge (in same Gaussian units).
b) They are magnetically excited neutrinos, subject to the same weak
interactions, and are thus able to influence the same nuclear phenomena. The most important observation is that contrary to neutrinos leptonic monopoles can be focused by electromagnetic forces
and their energy can be increased in magnetic fields.
Therefore, we can substitute the following reaction to the reaction
(2) :
p + m̃ → n + e+
(3)
Here m̃ is an anti-monopole with the same weak interactions as the
antineutrino in the reaction (2). Below we suggest a test experiment in
order to verify the reaction (3).
Some remarks :
1. Concerning the reaction (3). It may be objected that energy is not
conserved because a proton is lighter than a neutron. But that was
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G. Lochak
already the case for the β inverse formula (2) : such formulae are
only written in conformity with quantum rules, and the conservation of energy is admitted for other reasons. Our case is simpler
because the monopole may be accelerated in a magnetic field.
2. Concerning temperature. The temperature required must be enough to create a plasma, which is much lower than the several
hundred million degrees needed for other experiments in nuclear
fusion.
III. A test-experiment.
Leptonic magnetic monopoles generally appear in disruptive electric
phenomena in water, such as1 :
1. Explosion in water of a stepped up electric conductor (Urutskoiev,
Moscow, reproduced in Nantes, France).
2. Electric arc in water (Ivoilov, Kazan).
The monopoles are recorded in different manners, but most often on
photographic films. Here are three characteristic tracks : 1) The first
is greatly enlarged (characteristic caterpillar form). 2) The second is a
track with its image in a germanium mirror ; this image is identical to
the original rotated by an angle of π, in accordance with the theoretical
predictions. 3) The third track was observed on the magnetic north pole ;
a solar monopole created by a β decay in a strong solar magnetic field.
We have hundreds of other different examples of tracks.
!
!
By definition, the recorded monopoles were originally present
in the source. Thus, these same monopoles were able to accelerate the
creation of deuterons, which is the first and principal stage of the hydrogen cycle :
p + p → 2 D + e+ + ν
(4)
1 There
are other situations, such as β radioactivity in a magnetic field.
!
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But at this point there occurs a “ forced ” reaction due to an antimonopole coming from outside, which then disappears in the reaction, according to a formula of the following type :
p + p + m̃ → 2 D + e+
(5)
A possible experiment could be to create, in a container of
water, the explosion of an electric conductor (as in Urutskoiev’s
experiments), or an electric arc (as in Ivoilov’s experiments).
Then, the proportion of heavy water must increase as the water
cools in the container.
I am aware that I am making several hypotheses here, but there is
no science without hypotheses and I accept responsibility. Nevertheless,
apart from other possible objections, one important question concerns
the number of produced monopoles, and thus the probability of the purported nuclear phenomena.
Despite that, at a first glance, the reaction (3) seems to be easy
to realize, there is a difficulty : the number of monopoles and
consequently the probability of the reaction. If the number of monopoles
produced by a source would correspond to the number of trajectories
observed in the figures above, this number would be very small and the
probability would be negligible.
But an important observation by Ivoilov, perhaps confirmed more
recently by Daniel and Sonia Fargue, shows that apart from the rare large
tracks generally observed, there are many other tracks which, contrary
to the preceding, come directly from the direction of the source. These
tracks are very thin and are easy to miss. Nevertheless, they have the
charge of a monopole and they probably constitute the hidden but most
significant emission of monopoles.
It seems that the first who observe (indirectly) these thin tracks was
Urutskoiev [10]. When he obtained the first photographs of large monopole tracks on photographic film (curiously in a plane perpendicular to
the direction of the monopole source), he tried to find 3D tracks in a
bubble chamber. But he was disappointed because instead of 3D tracks
he obtained a large white cloud. I now believe that this cloud consisted of
the extremely numerous thin tracks later identified by Ivoilov. Actually,
the large tracks correspond to deviated monopoles that strike the limit
between the plastic film support and the photosensitive coating, and are
strongly deviated from their initial trajectory. The large tracks are thus
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due to a kind of rare “ accidents ”, which explains why they are so rare.
On the contrary the “true” tracks (“true” because they are free) seem
to be the numerous thin tracks.
Therefore, it seems that we can assert that the emitted monopoles are
actually not few but instead extremely numerous. Thus, it is possible
that my test-experiment might be not so difficult to perform.
Some other arguments lend support this idea, among which the macroscopic phenomena observed by Urutskoiev’s group after the Tchernobyl catastrophe2 , for example the following :
a) In the same hall there were two parallel conductors separated by
some meters : one was a water pipe coming from the nuclear reactor, and
the other an electric cable in a concrete boxing. During the catastrophe,
this concrete protection was broken by the strength of the electric cable
strongly attracted by the water pipe. Puzzled by this phenomenon a
young physicist emitted, just as a joke, the audacious hypothesis that
there could be magnetic monopoles in the water coming from the reactor. Actually, it was later confirmed, but this implies an enormous
quantity of monopoles.
b) The reactor had a concrete cover weighing about 3000 tons. During
the catastrophe, it was pushed aside and fell vertically against the wall
of the reactor. If this was due to gas pressure inside the reactor, then
a calculation proves that the walls would have exploded, whereas in
fact the walls of the reactor were in perfect condition. The paint on the
inside of these walls was not even burned, and it would have burned
at a temperature of just 300˚C. Two conclusions emerged from these
observations :
c) There was no fire in the reactor except in a very limited volume
(this was, of course, later verified directly) and thus no strong pressure.
d) If the cover was lifted, this means that its weight was far less than
3000 tons during the catastrophe. It was assumed that monopoles have
2 It must be emphasized that we absolutely disagree with the official Soviet interpretation of the catastrophe as the result of “ errors ” of engineers. We have strong
arguments in favor of the hypothesis of an explosion of an electrical machine (probably a transformer) which produced a stream of monopoles that then activated a chain
of disintegrations never seen before. An important point is that this hypothesis
was emitted independently from myself : we met only several years later.
It must be added that two completely independent groups were sent to Tchernobyl in
order to explain the catastrophe : one by a scientific center, the Kurtchatov Institute,
under the direction of Urutskoiev, and the other, the official one, in order to find a
guilty party. And this is the origin of the official “ explanation ”.
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modified gravitation. This was confirmed experimentally by Urutskoiev
and theoretically by myself, on the basis of my theory of monopoles and
of de Broglie’s theory of light which gives a quantum theory of gravitation
(de Broglie proved the influence of electromagnetism on gravitation, i.e.
the Einsteins’ unitary theory, in 1942 in his General Theory of Spin Particles. All this would be impossible unless an enormous quantity
of monopoles was produced.
Two last remarks.
1) Urutskoiev is skeptic concerning the tokamak because it is unstable. Concerning the known tokamak, he is right, he was even among
those who proved it. But I speak of a tokamak only in the sense of the russian acronym : “ tokamak ” means “ toroidal magnetic room ”. It
is really unstable with electric particles like protons which rotate around
the magnetic field, but I speak of anything else : a tokamak in which are
introduced not electric particles but magnetic monopoles which rotate
not around but along the magnetic field. It is another device : a monopole
accelerator for which I have a patent with my colleague Maurice Bergher
(deposit : Paris 23-7-2008, N˚08-55034). But, despite that I worked during a long time on accelerators, I must confess that I have not examined
the stability in this case. It remains to be done.
2) I disagree with my friend Urutskoiev when he asserts that we still
know very few about monopoles. I beg his pardon but I see in this assertion a small mania of an experimentor who does not believe in theory !
Let me recall that I have predicted the existence and main properties of
the leptonic monopole, on the theoretical basis of Dirac’s equation of the
electron (and not all on his calculations including a monopole) : I have
found Wave equations, mass nullity (contrary to the heavy monopoles
often predicted but never observed), symmetriy laws (in accordance with
the Pierre Curie), magnetic charge (that I deduced from physical symmetriy laws and not by an algebraic artifice), weak (and not strong)
interactions of the leptonic monopoles which I defined as magnetically
excited neutrinos, but their weak interactions are focusable owing to their
magnetic charge. Most of my theoretical predictions were experimentally
verified. If some are not, the responsability is the one of experimenters,
not mine. Anyway, I think that one cannot assert that we know nothing
or even “ few ” on monopoles ! Three hundred years after Newton, everybody believes in the primacy of experiment but it is a fact that theory
can precede it ; and here, we are in such a case.
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IV. Magnetic leptonic monopoles, a brief summary
(see Literature).
Consider the Dirac matrices γµ (µ = 1, ..., 4) and the Clifford matrices built on them :
ΓN = {I , γµ , iγµ γν , iγµ γ5 , γ5 = γ1 γ2 γ3 γ4 } (N = 1, ..., 16)
(6)
The following relations hold between the ΓN (in which the sign ± depends onµ and N :
γµ ΓN γµ = ± ΓN
(7)
It is easy to show that only two ΓN matrices commute in the same
manner with the four matrices γµ , namely Γ1 = I (with a + sign) and
Γ16 = γ5 (with a – sign : they anticommute).
a) The first matrix Γ1 = I defines a phase- (or gauge-) invariance :
ψ → eiϑ ψ
(8)
This invariance leads to the invariance of the free Dirac equation, with
a mass term but without external field :
m0 c
=0
(9)
γµ ∂µ ψ +
~
Owing to the preceding gauge invariance (8), a covariant derivation and
a local gauge invariance may be deduced, with Lorentz potentials (their
polar character is a consequence of the gauge) :
∇µ = ∂µ − i
e
Aµ ; ψ → ei
~c
e
~c
φ
ψ , Aµ → Aµ + ∂µ φ
from which the Dirac equation of the electron follows :
e
m0 c
γµ ∂µ − i Aµ ψ +
ψ=0
~c
~
(10)
(11)
b) The second matrix Γ16 = γ5 defines a new gauge invariance :
ψ → ei
e
~c
γ5 ϑ
ψ
(12)
Like the first one, it leads to the invariance of the free Dirac equation,
but without mass term because of the minus sign in (7) :
γµ ∂µ ψ = 0
(13)
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From the second gauge invariance (12) (see the references) we obtain a
second local invariance which no longer includes the Lorentz potentials
Aµ but instead pseudo-potentials Bµ :
∇µ = ∂µ − i
g
γ5 Bµ ; ψ → ei
~c
e
~c
γ5 φ
ψ ; Bµ → Bµ + ∂µ φ
(14)
From this, I have deduced the equation of the leptonic magnetic monopole [7, 8, 17] which is massless because of the minus sign in (7) :
g
γµ ∂µ − −i
γ5 Bµ ψ = 0
~c
(15)
This equation is generally used to describe the leptonic monopole, and
its predictions are experimentally verified. It automatically includes the
symmetry laws discovered by Maxwell and Pierre Curie. I have found
two other more complicated equations which obey the same
symmetry laws but with a non linear mass term,
The variance of the pseudo-quadri-potentials Bµ and φ in (14) is a
consequence of the pseudo-scalar matrix γ5 . For the same reason, the
magnetic charge g becomes a true scalar, like all physical constants,
and not a pseudo-scalar as in all the other monopole theories : in the
present theory, the chirality of magnetism is no longer expressed through
the physical constant g(which is scalar), but through a charge operator
G = g γ5 , in the spirit of all quantum theories.
We know that (10) leads to the conservation of electricity Jµ by the
Dirac equation (11) :
∂µ Jµ = 0
Jµ = iψ γµ ψ
(16)
All the same, the equation (15) implies, in virtue of (14), the conservation
of the magnetic current :
∂µ Σµ = 0
Σµ = iψ γµ γ5 ψ
(17)
The currents Jµ and Σµ are related by the algebraic formulae :
Jµ Σµ = 0 ; −Jµ Jµ = Σµ Σµ = Ω21 + Ω22
=
Ω=
1 ψ ψ ; Ω2 − iψ γ5 ψ
(18)
Ω1 and Ω2 are the Dirac invariant and pseudo-invariant respectively. It
follows from (18) that the electric current Jµ is time-like, as might be
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G. Lochak
expected. On the contrary, the magnetic current Σµ is space-like, which
is surprising. But all is cleared up in the Weyl representation :
1
ξ
ψ = √ (γ4 + γ5 )
(19)
η
2
This equation (19), defining the two-component spinors ξ and η, enables
us to break (15) into two independent left and right equations which
generalize the Weyl form of the neutrino equations [8, 17] :
1
c
1
c
∂
g
− s .∇ − i
(W + s . B) ξ = 0
∂t
~c
∂
g
+ s .∇ + i
(W − s . B) η = 0
∂t
~c
(20)
The kinetic parts of these equations are the two-component monopole
and anti-monopole, while the potential parts represent the electromagnetic interaction of a left and a right magnetic charge respectively. But
it must be emphasized that the kinetic parts of (20) are nothing but
the two-component of the left and right equations of a massless neutrino
(here applied to spinors).
The difference between a neutrino and a leptonic monopole is not
between the free particles, but only between their interactions with an
electromagnetic field : this interaction does not exist for the neutrino,
but for the leptonic monopole it corresponds to a plus or minus magnetic
charge according to the left and right symmetry.
This is why it is precisely the Weyl representation (20) of
the leptonic monopole that allows us to assert that the particles
that we call monopoles are, in fact, magnetically excited forms
of a neutrino and an antineutrino, subject like them to weak
interactions and opposite magnetic charges [8, 9, 17, 21].
Here, the s are the Pauli matrices and we have iBµ = {B , i W },
where B and W are a pseudo-vector and a pseudo-scalar in R3 ; B4 = W
is real because Bµ is axial. One can show that there are two isotropic
conservative left and right currents related to electricity and magnetism :
Xµ = ξ + ξ , −ξ + s ξ ; Yµ = η + η , η + s η ;
(21)
Jµ = Xµ + Yµ ; Σµ = Xµ − Yµ ; ∂µ Xµ = 0 ; ∂µ Yµ = 0
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165
Here Jµ is the sum of isotropic currents and it is time-like, while on
the contrary, Σµ is the difference of the same currents and is space-like
2
since Xµ Yµ = 4 |ξ + η| ≥ 0.
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(Manuscrit reçu le 18 septembre 2014)